1. Field of the Invention
The present invention relates to solid immersion lenses, especially to such solid immersion lenses to increase and optimize the spatial resolution and light collection efficiency of optical imaging and collection systems.
2. Description of Related Art
Optical spatial resolution is defined as the ability of an imaging system to clearly separate closely placed structures. Optical resolution is of particular importance for those who image objects in applications such as optical metrology, lithography and astronomy.
In an ideal world optical imaging elements would have infinite size where the maximum amount of light could be focused onto and/or collected from the object under investigation. The wave of nature of light combined with the limited aperture of optical elements lead to diffraction B the interference of light as it scatters from the discontinuity and recombines with the light was transmitted from other areas of the optical element.
In reality optical elements are limited size and light waves diffract as they travel through these elements and recombine from the aperture of these elements. Spatial resolution in real optical systems is adversely impacted by aberrations of the optical elements with finite aperture, fields of view and their material properties, amongst other factors.
There are many elements that need to be understood and compensated to optimize the performance of an optical system. Ideally optical elements would be impervious to the different wavelengths (color) of light and thereby not impact resolution and optical performance by chromatic aberrations. Ideally these elements would also be impervious between the light transmitted and focused at the areas close to their axis (paraxial), as opposed to those transmitted and focused further from their axis. This variation for radially symmetric elements is called spherical aberration. For a review of the aberrations, amongst others, their classification, and methods to properly compensate and optimize an optical imaging system the reader may refer to classical texts on optics.
In the following we will describe an optical element and method of use to enhance and increase the resolution capabilities of high-resolution imaging with minimal aberration correction to image objects and structures embedded in the material through the sample.
Even the best optimally designed optical system where the aberrations have been properly addressed and minimized the ultimate limitation is finite aperture size of the system leading to diffraction. Therefore we will focus our attention on diffraction-limited (resolution only limited by diffraction) optical systems. Various analytical expressions have been developed to define spatial resolution in a diffraction-limited system of an optical imaging system. These formulae and expressions all relate the fundamental properties of the illuminating light and the ability of the imaging system to couple into and collect light from the sample. For example, one way to use analytical expression for the resolution is to define the lateral spatial resolving power of an optical system is to resolve a grating of period T with a lens capable of focusing and collecting light within a half-cone θ0 (FIG. 10a):T=αλ0/(n*sin θ0)  (1)
Wherein λ0 is the wavelength of light in vacuum and An@ is the refractive index of the medium (i.e. for air n0=1, λ=λ0 the wavelength of light in air/vacuum. For a medium of refractive index n, λ=λ0/n). The proportionality constant, α, is defined by the resolution criteria, i.e. α=0.61 in the often-used Rayleigh resolution criterion, or α=0.5 for the Sparrow resolution criterion, amongst other oft used criterion. The maximum half-angle of the cone of light relates to the numerical aperture (NA), of the lens according to:NA=n*sin θ0  (2)Therefore one obtains the relationship:T=αλ0/(NA)  (3)
Consequently, efforts to increase spatial resolution have concentrated on either increasing the NA or using a light of a shorter wavelength. The NA can be increased by proper designing of the objective to increase the solid angle cone of light that is focused and collected to and from the sample, while reducing the wavelength is achieved by using a different illuminating source, for example, a laser light source or a narrow-filtered broad spectrum light source of for a shorter wavelength.
In the case where the structure under investigation is embedded in a material with an index of refraction n0, due to refraction, the half-cone angle inside the material (θ1) is related through half-cone angle in air (θ0) (FIG. 10b) through the expressionn0 Sin(θ0)=n1 Sin(θ1)(FIG. 10b)  (4)
Although the (sinus of the) cone angle is reduced by a factor of n0/n1, the wavelength is also reduce by the same factor. Therefore the NA is conserved, and the effective resolution of the imaging system remains unchanged. However the off normal incident (axis) rays bending at the air-medium interface introduce spherical aberrations and axial coma, which in turn reduce the image fidelity and overall resolution.
It must also be noted that in any imaging system the ability to maximize coupling and collection light onto and from the sample under inspection is critical to the imaging performance. Since more light focused and collected from the area of interest translate into larger signal (information). When the area of interest is embedded in a material, light reflected from the sample and incident on the material-air interface outside of the critical angle (θ0=sin4(n0/n1)) is reflected back into the sample (total internal reflection) and is not collected.
In summary, the larger difference between the refractive indices of the imaging system and the embedded object the smaller the cone angle of focus and the higher the total internal reflection (loss of light from the sample). Therefore the goal is to reduce and compensate for the abrupt transition in refractive indices between the lens focusing element (i.e. microscope objective) and the embedded object. The optimum would be to ‘match’ the refractive indices.
Traditionally to compensate for this reduction in resolution and collection the air gap between the objective lens and sample is filled with a fluid with a refractive index matching to that of the material, “index-matching fluid”. In many microscopes built for biological studies, the specimen is under a cover glass with a refractive index close (˜1.5) to that of the sample. The index-matching fluid used to Abridge@ between the cover-glass and embedded specimen would match as nearly as possible to the refractive indices. The objective lens in this index-matching set-up is also designed and optimized to image through the higher index fluid.
The enhancement in resolution with liquid is limited by the index of refraction of the fluid being used. The index of refraction of silicon is approximately 3.5, whereas the index of refraction of index-matching fluids is approximately 1.6. If the interface between the lens and the object is removed, then the NA of the optics can take full advantage of the higher index of refraction of transparent solid material. For example, in the case of silicon, the index of refraction is approximately 3.5. In cases where matching the refractive index of the material is not possible (for reason such as availability of fluids with matching refractive index or operational and implementation considerations), the ‘matching’ is achieved with a solid material. Obviously a primary ‘index-matching’ candidate material would be an element constructed from the same material as that of the object under study.
Although the goals are similar for solid index matching and fluid index matching (increasing the coupling and collection of light into and out of the sample) there is a major difference in their implementation and constraints on the overall optical system. Whereas fluids are malleable and easily fill in the gap between the lens and object, solid immersion elements must be designed to physically fit in and optically match to the imaging system. With the flat sample-air interface and the goal to couple over the largest solid angle (and not simply to extend the light further into space) the traditional solid immersion optical element by its nature is designed with a flat (interface to the sample) and symmetric curved convex surface (away from the sample). This curved surface could be a cylinder (e.g. U.S. Pat. No. 4,625,114) or a spherical design (e.g. U.S. Pat. No. 4,634,234) and because of its curvature acts as a positive focusing lens, thereby aptly called solid immersion lens (SIL). The SIL is very similar to the first (looking from the sample) plano-convex focusing/collection element in many traditional microscopic objectives. Whereas liquid matching is only a light coupling mechanism, solid immersion has a fixed focusing aspect in addition.
Of course, one may use both immersion techniques, i.e., use solid immersion lens and index matching fluid. The use of the above techniques is disclosed in, for example U.S. Pat. Nos. 3,524,694, 3,711,186, and 3,912,378 and Modern Optical Engineering, Warren J. Smith, McGraw-Hill, pp. 230-236, 1966. More modern discussions of immersion lenses can be found in U.S. Pat. Nos. 5,004,307, 5,208,648, and 5,282,088. For a proper understanding of the novel and advantageous features of the present invention, the reader is especially encouraged to review the later three patents, and Solid Immersion Microscopy, M. Mansfield, Stanford University Doctoral Thesis G.L. Report 4949, March 1992.
Prior art solid immersion lenses are plano-convex. That is, the bottom surface, i.e., the surface facing the object, is flat, while the top surface, i.e., the surface facing the objective lens is convex. FIGS. 1a-1c depict three immersion lenses corresponding to the later cited three patents. In FIGS. 1a-1c, the object to be imaged is identified as 100. FIGS. 1a and 1b correspond to the class solid immersion lenses that could be called normal incident hemispheres, whereas 1c is an aplanatic focusing element.
The immersion lens, 110, depicted in FIG. 1a is a hemisphere. That is, the flat surface of the plano-convex lens passes at the radial geometrical center, GC, of the upper hemispherical surface. Notably, all the light rays are perpendicular to the convex surface at the point of entry/exit. In U.S. Pat. No. 5,004,307 lens 110 is described as being further ground as exemplified in FIG. 1a by broken lines 111. This is done in order to allow for mounting, but does not affect the optical properties of the lens as being a hemisphere, as explained by one of the inventors in his Ph.D. Dissertation, Solid Immersion Microscopy, M. Mansfield, Stanford University, March 1992.
On the other hand, the flat surface of the lens, 120, depicted in FIG. 1b passes Aabove@ the radial geometrical center, GC of the upper surface. Notably, it is designed so that its geometrical center is at the focus point inside the object to be imaged. That is, lens 120 is used to image features embedded inside of a transparent object 100. In order to create continuity of index of refraction, it is suggested to use index matching material 125. In this configuration, light rays are perpendicular to the convex surface at the point of entry/exit (Note: in U.S. Pat. No. 5,208,648 the rays are depicted at an angle other than 90°; however, the present inventors believe otherwise. For example, compare the drawings in the >648 patent to those in the above cited Dissertation).
Another variation is depicted in FIG. 1c, wherein the flat surface passes Abelow@ the radial geometrical center, GC, of lens 130. The location of the flat surface is determined from the index of refraction of: the lens, the material surrounding the lens, and the object to be imaged. Such an immersion lens is referred to as Aaplanatic@ lens and is covered by U.S. Pat. No. 5,282,088 to Davidson, which is assigned to the assignee of this Application. In this configurations, light rays are not perpendicular to the convex surface at the point of entry/exit. As it can be seen from simple ray-tracing designs, the magnifying power of the “aplanatic” is stronger than the normal incident hemispheres.
In usage, the lenses depicted in FIGS. 1a-1c are Acoupled@ to the imaged object. That is, the lens is Acoupled@ to the object so as to allow communication of evanescent waves. In other words, the lenses are coupled to the object so that they capture rays propagating in the object at angles higher than the critical angle (the critical angle is that at which total internal reflection occurs). As is known in the art, the coupling can be achieved by, for example, physical contact with the imaged object, very close placement (up to about 200 nanometers) from the object, or the use of index matching material or fluid.
The prior art immersion lenses suffer from the following problems:
First, since the bottom surface is flat, it is difficult to pinpoint the location of the focus point, i.e., it is hard to specify exactly what point on the object is being imaged. This is an important issue when imaging very small objects, such as electronic circuits embedded in semiconductor (i.e. Silicon, or GaAs) devices.
Second, since the bottom surface is flat, it has a large contact area. That is, as is known in the prior art, one method of index matching without the use of an index matching fluid is to simply make the immersion lens contact the object to be imaged. However, such contact should be minimized when imaging sensitive semiconductor devices in order to avoid introducing defects, such as contamination and scratching.
Third, since the sample=s surface may not be perfectly flat (as is the case with semiconductors), the flat surface of the lens will basically have only a three-point contact with the sample=s surface. Consequently, it is difficult to ensure that the flat surface of the immersion lens is Aparallel@ and optically coupled to the surface of the sample over the entire area of contact.